We developed a random number generator consisting of twenty of HEMT chips which are flip-chip-bonded to a multilayer ceramic substrate with copper conductors. The thermal expansion is closely adjusted to that of GaAs from room to liquid nitrogen temperatures. The chip size are 5.0 to 8.2 mm square. Indium solder bumps were applied for bonding. The substrate size is 120 mm square and 4 mm thick. It has 16 thick-film layers at inner substrate and 2 thin-film layers on both polished outer-surfaces. The electric properties of the module were evaluated during operation in liquid nitrogen. The module stably generated random numbers at clock cycles as short as 1.49 ns in liquid nitrogen. Tests confirmed the higher switching speed of the HEMT at 77 K and also the high performance of the packaging where the substrate was composed of both a glass and an alumina-treated-zirconia powder (GAZ). The thermal expansion is closely adjusted to GaAs by the fine controlling of the glass to alumina-treated-zirconia powder ratio. Thermal shock tests from 300 K to 77 K were performed for the specimen of GAZ, alumina and fused silica. On the each of them, GaAs chips (5050.6 mm) were flip-chip-bonded with indium solder. The failure rate of the bondings increased related to the thermal-expansion difference between GaAs and the substrates (ΔTE) from 300 K to 77 K. Experimental results also indicated that the powder-ratio controlled GAZ is the more suitable for HEMT packaging as for the reliability of its bondings.